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X₁, X2,...,xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0x f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 03 at a significance level of a = 5%, determine : 1. Likelihood function L(x: 0) = f(x₁,x₂,...,xn10) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x₂,...,x₂100) and L(x: 0₁) = f(x₁,x₂,...,x₂0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00,0₁) with L (x: 00) 2(x: 0,0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80

X₁, X2,...,xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0x f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 03 at a significance level of a = 5%, determine : 1. Likelihood function L(x: 0) = f(x₁,x₂,...,xn10) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x₂,...,x₂100) and L(x: 0₁) = f(x₁,x₂,...,x₂0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00,0₁) with L (x: 00) 2(x: 0,0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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X₁, X2, Xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0* f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 0 # 3 at a significance level of a = 5%, determine : 1. Likelihood function L(x : 0) = f(x₁, x2, ...., Xñ[0) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x2,..., xn100) and L(x: 0₁) = f(x₁,x₂,..., xn|0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00, 0₁) with L (x: 00) 2(x: 00, 0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80
Transcribed Image Text:X₁, X2, Xn is a random sample from the population that follows a Poisson distribution with the density function: -0 0* f (x10) = ; x = 1,2,3,.... x! If you want to test Ho: 0 = 3 and Ho 0 # 3 at a significance level of a = 5%, determine : 1. Likelihood function L(x : 0) = f(x₁, x2, ...., Xñ[0) and the maximum likelihood estimator for 8 2. The Likelihood function under Ho and H₁, is L(x: 0o = f(x₁,x2,..., xn100) and L(x: 0₁) = f(x₁,x₂,..., xn|0₁) 3. Likelihood ratio statistics, namely: -2ln(x: 00, 0₁) with L (x: 00) 2(x: 00, 0₁) = L (x: 01) 4. test rejection area and give your conclusion if you have statistic Σ1 x = 80
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